To find the values of b and c that would make the equation x^2 + bx + c = 0 have roots equal to b and c, we can use the fact that the sum and product of the roots of a quadratic equation are related to its coefficients.

The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a, and the product of the roots is given by c/a.

In this case, we are given that the roots are b and c. So we have the following equations:

b + c = -b/a
bc = c/a

We can simplify the second equation by multiplying both sides by a:

abc = c

Now we have two equations:

b + c = -b/a
abc = c

We can solve these equations to find the values of b and c.

Solving the equations:
To solve the first equation, we can multiply both sides by a:

ab + ac = -b

Rearranging the equation, we get:

ab + b = -ac

Factoring out b, we have:

b(a + 1) = -ac

Dividing both sides by (a + 1), we get:

b = -ac/(a + 1)

Substituting this value of b into the second equation, we have:

abc = c

Replacing b with -ac/(a + 1), we get:

-a^2c/(a + 1) = c

Cross-multiplying, we have:

-a^2c = c(a + 1)

Simplifying, we get:

-a^2c = ac + c

Adding ac to both sides, we have:

ac - a^2c = c

Factoring out c, we get:

c(a - a^2) = c

Dividing both sides by c, we get:

a - a^2 = 1

This is a quadratic equation in terms of a. We can solve it by rearranging and factoring:

a^2 - a + 1 = 0

This equation does not have any real solutions. Therefore, there are no values of b and c that would make the equation x^2 + bx + c = 0 have roots equal to b and c.

Thus, the correct answer is option D) Both (a) and (b).